This course aims at covering advanced methods of numerical analysis. It briefs introduction to numerical computing, approximation and errors which is followed by methods of solving system of nonlinear equations and approximation of functions. Numerical solutions of ordinary differential equations; initial value problems and boundary value problems, simultaneous differential equations, Runga-Kutta methods, finite difference method. Numerical solution techniques for linear, elliptic, parabolic and hyperbolic partial differential equations. Methods will be implemented using toolboxes of MATLAB.